CN108426384B - Design method of two-stage thermal coupling type high-frequency pulse tube refrigerator for realizing cold quantity distribution - Google Patents

Design method of two-stage thermal coupling type high-frequency pulse tube refrigerator for realizing cold quantity distribution Download PDF

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CN108426384B
CN108426384B CN201810020609.3A CN201810020609A CN108426384B CN 108426384 B CN108426384 B CN 108426384B CN 201810020609 A CN201810020609 A CN 201810020609A CN 108426384 B CN108426384 B CN 108426384B
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CN108426384A (en
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党海政
谭军
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Shanghai Institute of Technical Physics of CAS
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F25—REFRIGERATION OR COOLING; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS; MANUFACTURE OR STORAGE OF ICE; LIQUEFACTION SOLIDIFICATION OF GASES
    • F25B—REFRIGERATION MACHINES, PLANTS OR SYSTEMS; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS
    • F25B9/00—Compression machines, plants or systems, in which the refrigerant is air or other gas of low boiling point
    • F25B9/14—Compression machines, plants or systems, in which the refrigerant is air or other gas of low boiling point characterised by the cycle used, e.g. Stirling cycle
    • F25B9/145—Compression machines, plants or systems, in which the refrigerant is air or other gas of low boiling point characterised by the cycle used, e.g. Stirling cycle pulse-tube cycle

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Abstract

The invention discloses a design method of a two-stage thermal coupling type high-frequency pulse tube refrigerator for realizing cold quantity distribution, which comprises the following eight steps: 1) the two-stage thermal coupling type high-frequency pulse tube refrigerator is equivalent to an alternating current circuit; 2) calculating the relationship between the dynamic pressure and the volume flow rate of inlets of the first-stage pulse tube cold finger and the second-stage pulse tube cold finger; 3) calculating the net refrigerating capacity of the first stage cold finger; 4) calculating the second-stage net refrigerating capacity; 5) giving an initial value of a cold finger parameter of the second-stage vessel and calculating; 6) calculating the impedance range and the total refrigerating capacity of the first-stage pulse tube cold finger; 7) giving an initial value of a first-stage vessel cold finger parameter and calculating; 8) the thermal bridge length and cross-sectional area are calculated. The design method of the two-stage thermal coupling type high-frequency pulse tube refrigerator capable of realizing cold quantity distribution has positive significance for practical development of the two-stage pulse tube refrigerator in the special fields of aerospace, superconduction and the like.

Description

Design method of two-stage thermal coupling type high-frequency pulse tube refrigerator for realizing cold quantity distribution
Technical Field
The invention relates to the field of refrigeration and low-temperature engineering, in particular to a design method of a two-stage thermal coupling type high-frequency pulse tube refrigerator for realizing cold quantity distribution.
Background
The pulse tube refrigerator is a great innovation of a regenerative low-temperature refrigerator, cancels a cold end discharger widely applied to the conventional regenerative low-temperature refrigerator (such as a Stirling refrigerator and a G-M refrigerator), and realizes low vibration, low interference and no abrasion of the cold end; through important improvement on structure optimization and phase modulation modes, the actual efficiency of a typical temperature zone also reaches the highest value of a regenerative low-temperature refrigerator. The remarkable advantages enable the pulse tube refrigerator to become a hot door for low-temperature refrigerator research in nearly 30 years, and the pulse tube refrigerator is widely applied to the aspects of aerospace, low-temperature electronics, superconducting industry, low-temperature medical industry and the like.
In practical application, different cooling capacities are often required to be provided at different temperature zones simultaneously. For example: for many cryogenic devices, some have two components operating at different temperatures, and some require cooling of both the detector and the optics, since background thermal noise is minimized only when the optics are cooled to a certain temperature, thereby significantly improving detection accuracy. Even some devices require simultaneous cooling of superconducting devices in different temperature zones. In many applications, it is generally recommended to use two single-stage pulse tube refrigerators to provide two different refrigeration temperatures, considering that the technology of the single-stage pulse tube refrigerator is still mature. However, a two-stage pulse tube refrigerator that requires only one compressor drive provides significant advantages in terms of weight, compactness, and system integration.
According to different coupling modes between the two stages of cold fingers, the two stages of pulse tube refrigerators can be divided into a thermal coupling type and an air coupling type. Gas coupling type gas split occurs at the cold end of the first stage, and gas distribution under low temperature conditions is much more complex than that under normal temperature. And for the heat coupling type, the gas dividing positions of the first stage cold finger and the second stage cold finger are the outlet of the compressor and are the normal temperature ends, so that the gas distribution is simple compared with the low-temperature environment. In addition, the phenomenon of mixed flow in the first-stage airflow and the second-stage airflow also occurs in the air-coupled two-stage pulse tube refrigerator, so that the stability of the air-coupled two-stage pulse tube refrigerator is greatly reduced. In summary, in the research and application of two-stage high-frequency pulse tube refrigerators oriented to the aspects of aerospace, superconduction and the like, the stability of the system is an extremely important consideration. Therefore, a two-stage high-frequency pulse tube refrigerator of a thermal coupling type is more suitable.
Because only a single compressor is used for driving, the refrigerating temperature and quality required to be provided by each stage of cold finger also need to be determined according to actual conditions. Therefore, a two-stage heat coupling type high-frequency pulse tube refrigerator capable of realizing interstage cold quantity distribution and a design method thereof are necessary for practical design and application.
Disclosure of Invention
In view of the defects of the prior art, the invention provides a design method of a two-stage thermal coupling type high-frequency pulse tube refrigerator for realizing cold quantity distribution.
The invention aims to provide a design method of a two-stage thermal coupling type high-frequency pulse tube refrigerator for realizing cold quantity distribution. The two-stage thermal coupling type high-frequency pulse tube refrigerator can be reasonably designed by the design method, the distribution of the two-stage cold quantity according to the requirement is realized, and the practical range of the two-stage high-frequency pulse tube refrigerator is greatly improved. The design method comprises the following steps:
the method comprises the following steps: the two-stage thermal coupling type high-frequency pulse tube refrigerator comprises a linear compressor 1, a connecting tube 2, a first-stage hot end heat exchanger 3, a first-stage regenerator 4, a first-stage cold end heat exchanger 5, a first-stage pulse tube 6, a first-stage inertia tube 7, a first-stage air reservoir 8, a second-stage hot end heat exchanger 9, a second-stage high-temperature section regenerator 10, a heat bridge 11, a second-stage intermediate heat exchanger 12, a second-stage low-temperature section regenerator 13, a second-stage cold end heat exchanger 14, a second-stage pulse tube 15 and a second-stage air reservoir 17, wherein the first-stage hot end heat exchanger 3, the first-stage regenerator 4, the first-stage cold end heat exchanger 5, the first-stage pulse tube 6, the first-stage inertia tube 7 and the first-stage air reservoir 8 form a first-stage pulse tube cold finger 18, the second-stage hot end heat exchanger 9, the secondary air reservoir 17 forms a second-stage pulse tube cold finger 19, the linear compressor 1 is respectively connected with the first-stage pulse tube cold finger 18 and the second-stage pulse tube cold finger 19 through the connecting pipe 2, and the first-stage pulse tube cold finger 18 and the second-stage pulse tube cold finger 19 are connected through the thermal bridge 11; according to the circuit analogy model, the pressure in the two-stage thermal coupling type high-frequency pulse tube refrigerator is equivalent to electromotive force, the volume flow rate is equivalent to current, the flow resistance, the flow capacity and the inertia are respectively equivalent to resistance, capacitance and inductance in a circuit, and the whole cold finger of the two-stage thermal coupling type high-frequency pulse tube refrigerator can be equivalent to an alternating current circuit;
step two: step two: the first stage pulse tube cold finger 18 and the second stage pulse tube cold finger 19 are in parallel relation in the circuit, the dynamic pressure at the inlet of the two cold fingers is equal, and the volume flow rate at the inlet is inversely proportional to the impedance value of the cold fingers, which can be expressed as:
p1-0＝p2-0＝p0(1)
Figure GDA0002385323060000031
Figure GDA0002385323060000032
p in the expression (1)1-0Is the dynamic pressure at the inlet of the first stage pulse tube cold finger 18, p2-0Is the dynamic pressure at the inlet of the second stage pulse tube cold finger 19, p0For the dynamic pressure at the outlet of the linear compressor 1, U in expression (2)1-0For the inlet of the first stage pulse tube cold finger 18Volumetric flow rate of (U)0Is the volumetric flow rate, Z, at the outlet of the linear compressor 11-0Is the impedance value, Z, of the first stage vessel cold finger 182-0For the impedance value of the second stage vessel cold finger 19, U in expression (3)2-0Is the volume flow rate at the inlet of the secondary vessel cold finger 19;
step three: the net cooling capacity available on the primary cold side heat exchanger 5, taking into account the additional inflow cold side enthalpy flow, conducted heat loss, and thermal bridge conduction, can be expressed as:
Figure GDA0002385323060000041
q in expression (4)c1Is the net refrigerating capacity, U, on the primary cold-side heat exchanger 51-2Is the volume flow rate, p, at the outlet of the primary regenerator 41-2Dynamic pressure at the outlet of the primary regenerator 4, η1-PTIs the vessel efficiency of the first-order vessel 6, theta1-2Is the phase difference between the dynamic pressure and the volume flow rate at the outlet of the primary regenerator 4, epsilon1-RGIs the effective coefficient, C, of the primary regenerator 4pAt a constant pressure specific heat capacity, pmIs the mean pressure, RgIs a gas constant, U1-1Is the volume flow rate, K, at the inlet of the primary regenerator 41-RGIs the heat conductivity coefficient of the primary regenerator 4, A1-RGIs the heat conduction sectional area of the primary regenerator 41-RGLength of primary regenerator 4, THIs the temperature of the hot end of the primary regenerator 4, T1Is the cold end temperature, A, of the first stage pulse tube cold finger 18strIs the heat conduction sectional area of the heat bridge 11, lambda is the heat conduction coefficient of the heat bridge material, TmidIs the temperature, L, of the secondary intermediate heat exchanger 12strIs the thermal bridge length;
step four: the net refrigeration available on the secondary cold side heat exchanger 14, taking into account the additional flow into the cold side enthalpy flow of the regenerator, conducted heat loss, and non-ideal gas effects, can be expressed as:
Figure GDA0002385323060000042
q in expression (5)c2Is the net refrigeration capacity, U, on the secondary cold side heat exchanger 142-4Is the volume flow rate, p, at the outlet of the secondary low-temperature section regenerator 132-4Dynamic pressure at the outlet of the secondary low temperature stage regenerator 13, η2-PTThe vessel efficiency, θ, of the secondary vessel 152-4Is the phase difference between the dynamic pressure and the volume flow rate at the outlet of the secondary low-temperature section cold accumulator 13, Z is the gas compression factor, epsilon2-RGIs the effective coefficient, C, of the secondary low-temperature section cold accumulator 13pAt a constant pressure specific heat capacity, pmIs the mean pressure, RgIs a gas constant, U2-1Is the volume flow rate, K, at the inlet of the secondary high-temperature section regenerator 102-RGIs the heat conductivity coefficient, A, of the secondary low-temperature section regenerator 132-RGIs the heat-conducting cross-sectional area of the secondary low-temperature section cold accumulator 132-RGIs the length, T, of the secondary low temperature section regenerator 13midIs the temperature, T, of the secondary intermediate heat exchanger 122The cold end temperature of the second stage pulse tube cold finger 19;
step five: setting the operation parameters of the second stage pulse tube cold finger 19 and the initial values of the parameters of each component, including; inflation pressure, operating frequency, refrigerating temperature, precooling temperature, length, diameter and slit size of a secondary hot-end heat exchanger 9, length, diameter, wall thickness, cold accumulation filler and filling mode of a secondary high-temperature section cold accumulator 10, length, diameter, wall thickness, cold accumulation filler and filling mode of a secondary low-temperature section cold accumulator 13, length, diameter and slit size of a secondary cold-end heat exchanger 14, length, diameter and wall thickness of a secondary pulse tube 15, length and diameter of a secondary inertia tube 16 and volume of a secondary air reservoir 17, refrigerating capacity, precooling capacity, input PV work, impedance and phase angle are calculated through a circuit analogy model, whether the refrigerating capacity meets the requirement is checked, if the refrigerating capacity meets the requirement, the step six is carried out, if the refrigerating capacity does not meet the requirement, initial parameter adjustment is carried out, and the step five is repeated;
step six: according to the impedance value and the impedance phase angle at the inlet of the second-stage pulse tube cold finger 19 and the correlation between the current and the voltage of the parallel circuit, which are obtained in the fifth step, the impedance size range and the impedance phase angle range of the first-stage pulse tube cold finger 18 under the condition of the specified output power can be obtained, and according to the precooling amount obtained in the fifth step and the requirement on the refrigerating capacity of the first-stage pulse tube cold finger 18, the total refrigerating capacity of the first-stage pulse tube cold finger 18 is obtained;
step seven: giving initial values of parameters of each component of the first-stage vessel cold finger 18, including; the length, the diameter and the slit size of the primary hot end heat exchanger 3, the length, the diameter, the wall thickness, the cold storage filler and the filling mode of the primary cold end heat exchanger 4, the length, the diameter and the slit size of the primary cold end heat exchanger 5, the length, the diameter and the wall thickness of the primary pulse tube 6, the length and the diameter of the primary inertia tube 7 and the volume of the primary air reservoir 8 are calculated according to a circuit analogy model, the impedance size, the phase angle and the refrigerating capacity of the primary pulse tube cold finger 18 are calculated, whether the impedance size and the phase angle meet the requirements in the step six or not is checked, whether the refrigerating capacity meets the requirements of the total refrigerating capacity in the step six or not is checked, if any one of the impedance size and the phase angle does not meet the requirements, the parameter initial values;
step eight: the length and the cross-sectional area of the thermal bridge are determined by the following relational expression (6) according to the magnitude of the pre-cooling capacity.
Figure GDA0002385323060000061
Q in expression (6)preFor pre-cooling amount, AstrIs the heat conduction cross-sectional area of the thermal bridge 11, lambda is the heat conductivity of the thermal bridge, T1For the first-stage pulse tube cold finger 18 refrigeration temperature, TmidIs the temperature, L, of the secondary intermediate heat exchanger 12strThe design is completed for the thermal bridge length.
The invention has the advantages that:
1) the design method of the two-stage heat coupling type high-frequency pulse tube refrigerator for realizing the interstage cold quantity distribution is provided, and the two-stage cold quantity distribution according to the requirement is realized;
2) the two-stage thermal coupling type high-frequency pulse tube refrigerator meeting the actual application requirements can be quantitatively designed by the method, and the two-stage pulse tube refrigerator can be widely applied.
The two-stage thermal coupling type high-frequency pulse tube refrigerator can be reasonably designed by the design method, the two-stage cold quantity can be distributed as required, and the practical range of the two-stage high-frequency pulse tube refrigerator is greatly enlarged.
Drawings
FIG. 1 is a flow chart of a design method of a two-stage thermal coupling type high-frequency pulse tube refrigerator capable of realizing cold quantity distribution;
FIG. 2 is a schematic structural diagram of a two-stage thermal coupling type high-frequency pulse tube refrigerator;
wherein: 1 is a linear compressor; 2 is a connecting pipe; 3 is a first-stage hot-end heat exchanger; 4 is a primary regenerator; 5 is a primary cold end heat exchanger; 6 is a primary vessel; 7 is a primary inertia tube; 8 is a first-level gas reservoir; 9 is a secondary hot end heat exchanger; 10 is a secondary high-temperature section regenerator; 11 is a thermal bridge; 12 is a secondary intermediate heat exchanger; 13 is a secondary low-temperature section cold accumulator; 14 is a secondary cold end heat exchanger; 15 is a secondary vessel; 16 is a secondary inertia tube; 17 is a secondary gas reservoir; 18 is a first stage vessel cold finger; and 19 is a second stage vessel cold finger.
Detailed Description
The following detailed description of the embodiments of the present invention is provided with reference to the accompanying drawings and examples:
FIG. 1 is a flow chart of the design method of the two-stage thermal coupling type high-frequency pulse tube refrigerator capable of realizing cold quantity distribution;
fig. 2 is a schematic structural diagram of a two-stage thermal coupling type high-frequency pulse tube refrigerator.
The design method comprises the following steps:
the method comprises the following steps: the two-stage thermal coupling type high-frequency pulse tube refrigerator comprises a linear compressor 1, a connecting tube 2, a first-stage hot end heat exchanger 3, a first-stage regenerator 4, a first-stage cold end heat exchanger 5, a first-stage pulse tube 6, a first-stage inertia tube 7, a first-stage air reservoir 8, a second-stage hot end heat exchanger 9, a second-stage high-temperature section regenerator 10, a heat bridge 11, a second-stage intermediate heat exchanger 12, a second-stage low-temperature section regenerator 13, a second-stage cold end heat exchanger 14, a second-stage pulse tube 15 and a second-stage air reservoir 17, wherein the first-stage hot end heat exchanger 3, the first-stage regenerator 4, the first-stage cold end heat exchanger 5, the first-stage pulse tube 6, the first-stage inertia tube 7 and the first-stage air reservoir 8 form a first-stage pulse tube cold finger 18, the second-stage hot end heat exchanger 9, the secondary air reservoir 17 forms a second-stage pulse tube cold finger 19, the linear compressor 1 is respectively connected with the first-stage pulse tube cold finger 18 and the second-stage pulse tube cold finger 19 through the connecting pipe 2, and the first-stage pulse tube cold finger 18 and the second-stage pulse tube cold finger 19 are connected through the thermal bridge 11; according to the circuit analogy model, the pressure in the two-stage thermal coupling type high-frequency pulse tube refrigerator is equivalent to electromotive force, the volume flow rate is equivalent to current, the flow resistance, the flow capacity and the inertia are respectively equivalent to resistance, capacitance and inductance in a circuit, and the whole cold finger of the two-stage thermal coupling type high-frequency pulse tube refrigerator can be equivalent to an alternating current circuit;
step two: the first stage pulse tube cold finger 18 and the second stage pulse tube cold finger 19 are in parallel relation in the circuit, the dynamic pressure at the inlet of the two cold fingers is equal, and the volume flow rate at the inlet is inversely proportional to the impedance value of the cold fingers, which can be expressed as:
p1-0＝p2-0＝p0(1)
Figure GDA0002385323060000081
Figure GDA0002385323060000082
p in the expression (1)1-0Is the dynamic pressure at the inlet of the first stage pulse tube cold finger 18, p2-0Is the dynamic pressure at the inlet of the second stage pulse tube cold finger 19, p0For the dynamic pressure at the outlet of the linear compressor 1, U in expression (2)1-0Is the volume flow rate at the inlet of the first stage pulse tube cold finger 18, U0Is the volumetric flow rate, Z, at the outlet of the linear compressor 11-0Is the impedance value, Z, of the first stage vessel cold finger 182-0For the impedance value of the second stage vessel cold finger 19, U in expression (3)2-0Is the volume flow rate at the inlet of the secondary vessel cold finger 19;
step three: the net cooling capacity available on the primary cold side heat exchanger 5, taking into account the additional inflow cold side enthalpy flow, conducted heat loss, and thermal bridge conduction, can be expressed as:
Figure GDA0002385323060000083
q in expression (4)c1Is the net refrigerating capacity, U, on the primary cold-side heat exchanger 51-2Is the volume flow rate, p, at the outlet of the primary regenerator 41-2Dynamic pressure at the outlet of the primary regenerator 4, η1-PTIs the vessel efficiency of the first-order vessel 6, theta1-2Is the phase difference between the dynamic pressure and the volume flow rate at the outlet of the primary regenerator 4, epsilon1-RGIs the effective coefficient, C, of the primary regenerator 4pAt a constant pressure specific heat capacity, pmIs the mean pressure, RgIs a gas constant, U1-1Is the volume flow rate, K, at the inlet of the primary regenerator 41-RGIs the heat conductivity coefficient of the primary regenerator 4, A1-RGIs the heat conduction sectional area of the primary regenerator 41-RGLength of primary regenerator 4, THIs the temperature of the hot end of the primary regenerator 4, T1Is the cold end temperature, A, of the first stage pulse tube cold finger 18strIs the heat conduction sectional area of the heat bridge 11, lambda is the heat conduction coefficient of the heat bridge material, TmidIs the temperature, L, of the secondary intermediate heat exchanger 12strIs the thermal bridge length;
step four: the net refrigeration available on the secondary cold side heat exchanger 14, taking into account the additional flow into the cold side enthalpy flow of the regenerator, conducted heat loss, and non-ideal gas effects, can be expressed as:
Figure GDA0002385323060000091
q in expression (5)c2Is the net refrigeration capacity, U, on the secondary cold side heat exchanger 142-4Is the volume flow rate, p, at the outlet of the secondary low-temperature section regenerator 132-4Dynamic pressure at the outlet of the secondary low temperature stage regenerator 13, η2-PTThe vessel efficiency, θ, of the secondary vessel 152-4Is the phase difference between the dynamic pressure and the volume flow rate at the outlet of the secondary low-temperature section cold accumulator 13, Z is the gas compression factor, epsilon2-RGIs the effective coefficient, C, of the secondary low-temperature section cold accumulator 13pAt a constant pressure specific heat capacity, pmIs the mean pressure, RgIs a gas constant, U2-1Is the volume flow rate, K, at the inlet of the secondary high-temperature section regenerator 102-RGIs the heat conductivity coefficient, A, of the secondary low-temperature section regenerator 132-RGIs the heat-conducting cross-sectional area of the secondary low-temperature section cold accumulator 132-RGIs the length, T, of the secondary low temperature section regenerator 13midIs the temperature, T, of the secondary intermediate heat exchanger 122The cold end temperature of the second stage pulse tube cold finger 19;
step five: setting the operation parameters of the second stage pulse tube cold finger 19 and the initial values of the parameters of each component, including; inflation pressure, operating frequency, refrigerating temperature, precooling temperature, length, diameter and slit size of a secondary hot-end heat exchanger 9, length, diameter, wall thickness, cold accumulation filler and filling mode of a secondary high-temperature section cold accumulator 10, length, diameter, wall thickness, cold accumulation filler and filling mode of a secondary low-temperature section cold accumulator 13, length, diameter and slit size of a secondary cold-end heat exchanger 14, length, diameter and wall thickness of a secondary pulse tube 15, length and diameter of a secondary inertia tube 16 and volume of a secondary air reservoir 17, refrigerating capacity, precooling capacity, input PV work, impedance and phase angle are calculated through a circuit analogy model, whether the refrigerating capacity meets the requirement is checked, if the refrigerating capacity meets the requirement, the step six is carried out, if the refrigerating capacity does not meet the requirement, initial parameter adjustment is carried out, and the step five is repeated;
step six: according to the impedance value and the impedance phase angle at the inlet of the second-stage pulse tube cold finger 19 and the correlation between the current and the voltage of the parallel circuit, which are obtained in the fifth step, the impedance size range and the impedance phase angle range of the first-stage pulse tube cold finger 18 under the condition of the specified output power can be obtained, and according to the precooling amount obtained in the fifth step and the requirement on the refrigerating capacity of the first-stage pulse tube cold finger 18, the total refrigerating capacity of the first-stage pulse tube cold finger 18 is obtained;
step seven: giving initial values of parameters of each component of the first-stage vessel cold finger 18, including; the length, the diameter and the slit size of the primary hot end heat exchanger 3, the length, the diameter, the wall thickness, the cold storage filler and the filling mode of the primary cold end heat exchanger 4, the length, the diameter and the slit size of the primary cold end heat exchanger 5, the length, the diameter and the wall thickness of the primary pulse tube 6, the length and the diameter of the primary inertia tube 7 and the volume of the primary air reservoir 8 are calculated according to a circuit analogy model, the impedance size, the phase angle and the refrigerating capacity of the primary pulse tube cold finger 18 are calculated, whether the impedance size and the phase angle meet the requirements in the step six or not is checked, whether the refrigerating capacity meets the requirements of the total refrigerating capacity in the step six or not is checked, if any one of the impedance size and the phase angle does not meet the requirements, the parameter initial values;
step eight: the length and the cross-sectional area of the thermal bridge are determined by the following relational expression (6) according to the magnitude of the pre-cooling capacity.
Figure GDA0002385323060000101
Q in expression (6)preFor pre-cooling amount, AstrIs the heat conduction cross-sectional area of the thermal bridge 11, lambda is the heat conductivity of the thermal bridge, T1For the first-stage pulse tube cold finger 18 refrigeration temperature, TmidIs the temperature, L, of the secondary intermediate heat exchanger 12strThe design is completed for the thermal bridge length.

Claims (1)

1. A design method of a two-stage thermal coupling type high-frequency pulse tube refrigerator for realizing cold quantity distribution is characterized by comprising the following steps:
the method comprises the following steps: the two-stage high-frequency thermal coupling type high-frequency pulse tube refrigerator comprises a linear compressor (1), a connecting tube (2), a first-stage hot end heat exchanger (3), a first-stage regenerator (4), a first-stage cold end heat exchanger (5), a first-stage pulse tube (6), a first-stage inertia tube (7), a first-stage air reservoir (8), a second-stage hot end heat exchanger (9), a second-stage high-temperature section regenerator (10), a thermal bridge (11), a second-stage intermediate heat exchanger (12), a second-stage low-temperature section regenerator (13), a second-stage cold end heat exchanger (14), a second-stage pulse tube (15), a second-stage inertia tube (16) and a second-stage air reservoir (17), wherein the first-stage hot end heat exchanger (3), the first-stage regenerator (4), the first-stage cold end heat exchanger (5), the first-stage pulse tube (6), the, The secondary high-temperature section cold accumulator (10), the secondary intermediate heat exchanger (12), the secondary low-temperature section cold accumulator (13), the secondary cold-end heat exchanger (14), the secondary pulse tube (15), the secondary inertia tube (16) and the secondary air reservoir (17) form a secondary pulse tube cold finger (19), the linear compressor (1) is respectively connected with the first pulse tube cold finger (18) and the second pulse tube cold finger (19) through the connecting tube (2), and the first pulse tube cold finger (18) is connected with the second pulse tube cold finger (19) through the thermal bridge (11); according to the circuit analogy model, the pressure in the two-stage high-frequency pulse tube refrigerator is equivalent to electromotive force, the volume flow rate is equivalent to current, the flow resistance, the flow capacity and the inertia are respectively equivalent to resistance, capacitance and inductance in the circuit, and the whole two-stage thermal coupling type high-frequency pulse tube refrigerator cold finger can be equivalent to an alternating current circuit;
step two: the first stage pulse tube cold finger (18) and the second stage pulse tube cold finger (19) belong to a parallel relation in the circuit, the dynamic pressure at the inlet of the two cold fingers is equal, and the volume flow rate at the inlet is inversely proportional to the impedance value of the cold fingers, and can be expressed as:
p1-0＝p2-0＝p0(1)
Figure FDA0002385323050000021
Figure FDA0002385323050000022
p in the expression (1)1-0Is the dynamic pressure at the inlet of the first stage pulse tube cold finger (18), p2-0Is the dynamic pressure at the inlet of the second stage pulse tube cold finger (19), p0Is the dynamic pressure at the outlet of the linear compressor (1), U in the expression (2)1-0Is the volume flow rate at the inlet of the first stage pulse tube cold finger (18), U0Is the volume flow rate, Z, at the outlet of the linear compressor (1)1-0Is the impedance value, Z, of the first stage vessel cold finger (18)2-0For the impedance value of the second stage vessel cold finger (19), expression (3)Middle U2-0Is the volume flow rate at the inlet of the secondary vessel cold finger (19);
step three: the net refrigerating capacity available on the primary cold end heat exchanger (5) under the condition of considering the enthalpy flow additionally flowing into the cold end of the regenerator, the heat conduction and the heat conduction of the heat bridge can be expressed as follows:
Figure FDA0002385323050000023
q in expression (4)c1Is the net refrigerating capacity, U, on the primary cold-end heat exchanger (5)1-2Is the volume flow rate, p, at the outlet of the primary regenerator (4)1-2Is the dynamic pressure at the outlet of the primary regenerator (4), η1-PTIs the vessel efficiency of the first-order vessel (6), theta1-2Is the phase difference between the dynamic pressure and the volume flow rate at the outlet of the primary regenerator (4), epsilon1-RGIs the effective coefficient of the primary regenerator (4), CpAt a constant pressure specific heat capacity, pmIs the mean pressure, RgIs a gas constant, U1-1Is the volume flow rate at the inlet of the primary regenerator (4), K1-RGIs the heat conductivity coefficient of the primary regenerator (4), A1-RGIs the heat conduction sectional area of the primary regenerator (4) |1-RGIs the length, T, of the primary regenerator (4)HIs the temperature of the hot end of the primary regenerator (4), T1Is the cold end temperature, A, of the first stage pulse tube cold finger (18)strIs the heat conduction sectional area of the heat bridge (11), lambda is the heat conduction coefficient of the heat bridge material, TmidIs the temperature, L, of the secondary intermediate heat exchanger (12)strIs the thermal bridge length;
step four: the net refrigeration available on the secondary cold side heat exchanger (14) taking into account the additional flow into the cold side enthalpy flow of the regenerator, conducted heat losses and non-ideal gas effects can be expressed as:
Figure FDA0002385323050000031
q in expression (5)c2Is the net refrigerating capacity, U, on the secondary cold side heat exchanger (14)2-4Is a secondary low-temperature section cold accumulator (13)Volumetric flow rate at the port, p2-4Is dynamic pressure at the outlet of the secondary low-temperature section cold accumulator (13), η2-PTIs the vessel efficiency of the secondary vessel (15), theta2-4Is the phase difference between the dynamic pressure and the volume flow rate at the outlet of the secondary low-temperature section cold accumulator (13), Z is a gas compression factor, epsilon2-RGIs the effective coefficient of a secondary low-temperature section cold accumulator (13), CpAt a constant pressure specific heat capacity, pmIs the mean pressure, RgIs a gas constant, U2-1Is the volume flow rate at the inlet of the secondary high-temperature section cold accumulator (10), K2-RGIs the heat conductivity coefficient of a secondary low-temperature section cold accumulator (13), A2-RGIs the heat conduction cross section area of the secondary low-temperature section cold accumulator (13) |2-RGIs the length T of the secondary low-temperature section cold accumulator (13)midIs the temperature, T, of the secondary intermediate heat exchanger (12)2The cold end temperature of the second stage pulse tube cold finger (19);
step five: setting the operation parameters of the second stage pulse tube cold finger (19) and the initial values of the parameters of each component, including; inflation pressure, operating frequency, refrigerating temperature, precooling temperature, the length, diameter and slit size of a secondary hot end heat exchanger (9), the length, diameter, wall thickness, cold storage filler and filling mode of a secondary high-temperature section cold accumulator (10), the length, diameter, wall thickness, cold storage filler and filling mode of a secondary low-temperature section cold accumulator (13), the length, diameter and slit size of a secondary cold end heat exchanger (14), the length, diameter and wall thickness of a secondary pulse tube (15), the length and diameter of a secondary inertia tube (16) and the volume of a secondary air reservoir (17), refrigerating capacity, precooling capacity, input PV work, impedance and phase angle are calculated through a circuit analogy model, whether the refrigerating capacity meets requirements is checked, if the refrigerating capacity meets the requirements, the step six is carried out, if the refrigerating capacity does not meet the requirements, the initial parameter is adjusted, and the step five is repeated;
step six: according to the impedance value and the impedance phase angle at the inlet of the second-stage pulse tube cold finger (19) and the correlation between the current and the voltage of the parallel circuit, which are obtained in the fifth step, the impedance size range and the impedance phase angle range of the first-stage pulse tube cold finger (18) under the condition of appointed output power can be obtained, and the total refrigerating capacity of the first-stage pulse tube cold finger (18) is obtained according to the precooling capacity obtained in the fifth step and the requirement on the refrigerating capacity of the first-stage pulse tube cold finger (18);
step seven: initial values of parameters of all parts of a first-stage vessel cold finger (18) are given, including; the length, the diameter and the slit size of a primary hot end heat exchanger (3), the length, the diameter, the wall thickness, the cold storage filler and the filling mode of a primary cold storage device (4), the length, the diameter and the slit size of a primary cold end heat exchanger (5), the length, the diameter and the wall thickness of a primary pulse tube (6), the length and the diameter of a primary inertia tube (7) and the volume of a primary air reservoir (8) are calculated according to a circuit analogy model, the impedance size, the phase angle and the refrigerating capacity of a primary pulse tube cold finger (18) are calculated, whether the impedance size and the phase angle meet the requirements in the step six is checked, whether the refrigerating capacity meets the requirements of the total refrigerating capacity in the step six is checked, if any one of the impedance size, the phase angle and the phase angle do not meet the requirements, the initial values of all the parameters of the primary pulse;
step eight: according to the magnitude of the precooling quantity, the length and the cross section area of the heat bridge are determined by the following relational expression (6),
Figure FDA0002385323050000041
q in expression (6)preFor pre-cooling amount, AstrIs the heat conduction sectional area of the heat bridge (11), lambda is the heat conduction coefficient of the heat bridge, T1Is the first-stage pulse tube cooling finger (18) refrigeration temperature, TmidIs the temperature, L, of the secondary intermediate heat exchanger (12)strThe design is completed for the thermal bridge length.
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